Most existing theoretical investigations of the accuracy of diffusion models, albeit significant, assume the score function has been approximated to a certain accuracy, and then use this a priori bound to control the error of generation. This article instead provides a first quantitative understanding of the whole generation process, i.e., both training and sampling. More precisely, it conducts a non-asymptotic convergence analysis of denoising score matching under gradient descent. In addition, a refined sampling error analysis for variance exploding models is also provided. The combination of these two results yields a full error analysis, which elucidates (again, but this time theoretically) how to design the training and sampling processes for effective generation. For instance, our theory implies a preference toward noise distribution and loss weighting that qualitatively agree with the ones used in [Karras et al. 2022]. It also provides some perspectives on why the time and variance schedule used in [Karras et al. 2022] could be better tuned than the pioneering version in [Song et al. 2020].

对于扩散模型的准确性进行了理论研究，通过梯度下降方法对去噪积分评分匹配的训练和采样过程进行了非渐近收敛分析，并提供了方差爆炸模型的抽样误差分析。通过这两个结果的结合，明确了如何设计有效生成的训练和采样过程。

评估扩散型生成模型的设计空间